# Relativistic length, 2 viewpoints

1. Sep 16, 2008

### pacu

Problem statement:

Two identical cyclists ride past each other with constant velocities Va and Vb, which are close to the speed of light. Can it be that cyclist A perceives cyclist B as shorter or longer that cyclist B percieves cyclist A ? Or simply La is NOT equal to Lb ? (La-length of cyclist A as seen by cyclist B, Lb -length of cyclist B as seen by cyclist A).

Relevant formulas:

Relative speed V = Va+Vb/(1+(Va*Vb/c^2))
Relative length l = lo * square root from 1-(V/c)^2

Conclusion:

The V from the second equasion is equal for both cyclists, since addition and multiplication are alternate. lo is also equal. So there is no difference in the way cyclists A and B see each other.

Is this conclusion right?

Last edited: Sep 16, 2008
2. Sep 16, 2008

### granpa

its correct if the cyclists are the same length to begin with.

dont forget that there is also a loss of simultaneity. once you factor that in it stops seeming so impossible.

Last edited: Sep 16, 2008